Claes Hedberg
Thesis title: Theoretical studies of nonlinear propagation of modulated harmonic sound waves
Date: November 14, 1994
Faculty opponent: Prof. Jacqueline Naze-Tjötta, Univ.
of Bergen, Norway
Evaluation Committee: Prof. Olle Brander, CTH, TeknD Ingemar
Lindblad, FFA, Prof. Anders Nilsson, KTH.
Main Advisor: Docent Bengt Enflo
A sufficiently strong sound source generates in a thermoviscous fluid
due to nonlinearity a frequency spectrum consisting of all multiples of
the original frequencies. This thesis is examining some of the
aspects of this generation
for plane waves propagating in a homogeneous medium.
The Burgers equation is used as a model and it is solved by
the saddle point method for a biharmonic boundary condition for
the region after shock formation. For higher intensity waves
the evolution is described in the dissipative free limit for
an amplitude-phase modulated initial signal.
The number of saddle points needed to obtain a solution differs
with the region and the demands on the detailed description of
the evolution. An attempt to minimize the number of saddle points
to one is made which gives a relatively simple calculations.
The influence of phase between the initial frequencies
is examined and is found to have no impact on the amplitude
of the Fourier coefficients. But when the ratio between the frequencies
is not an irrational number there is influence through the
summation of Fourier coefficients.
Claes will go to Austin, Texas for a post-doc position in
October 1995.
Nils Tillmark
Thesis title: Experiments on transition and turbulence in plane Couette flow
Date: May 19, 1995
Faculty opponent: Prof. Helmut Eckelmann, Institut für angewandte
Mechanik und Strömungs-physik, Universitet Göttingen.
Evaluation Committee: Prof. Håkan Gustavsson, LuTH, TeknD Torgny Lagerstedt, Alfa
Laval Separation AB, Prof. Rolf Karlsson, Vattenfall Utveckling AB.
Main Advisor: Prof. Henrik Alfredsson
The thesis is concerned with the problem of
plane Couette flow that is one of the canonical shear flows for which
hitherto only a limited number of experimental studies have been carried
out. Various aspects of plane Couette flow using mainly experimental
techniques are reported. It is shown that the plane Couette flow has a
transitional Reynolds number around 360 which is lower than in channel or
pipe flow and that transition may occur
through the formation of turbulent spots. The turbulent spot is studied and
its spreading
rate in the spanwise as well as in the streamwise directions are determined
over a range
of Reynolds numbers. At the wing-tips of the spot streamwise elongated
waves are
observed moving in the direction from the spot centre. The flow outside
the wing-tips is found to be forced in the spanwise direction as the spot
is expanding
and that the spanwise velocity profile is inflectional.
The decay of laminar plane Couette flow is studied and shown
to be susceptible to a Rayleigh instability. Calculations as well as visual
techniques show that the flow develops stationary spanwise longitudinal
roll-cells occupying the whole height of the channel.
Long time one point statistic measurements of the streamwise
velocity component show that the flow in regions close to the walls is very
similar to other channel flows whereas in the centre of the channel the
turbulence level is almost constant and more than twice as high.
Two-point correlation measurements and autocorrelations in the
central region
show that the flow
contains very large scale structures in the
streamwise direction with regular spanwise periodicity.
Comparisons between experimentally and numerically obtained
databases are performed. Turbulence producing events in the buffer region
are isolated, using VITA and VISA techniques. Detailed analysis of the
VISA events and extensive comparisons with similar numerical data base for
plane Poiseuille are made.